Speeding Up Bellman Ford via Minimum Violation Permutations

The Bellman-Ford algorithm is a basic primitive for computing single source shortest paths in graphs with negative edge-weights. Its running time is governed by the order the algorithm examines vertices for iterative updates on the value of their shortest path. In this work we study this problem through the lens of 'Algorithms with Predictions,' and show how to leverage auxiliary information from similar instances to improve the running time. We do this by identifying the key problem of Minimum Violation Permutations, and give algorithms with strong approximation guarantees as well as formal lower bounds. We complement the theoretical analysis with an empirical evaluation, showing that this approach can lead to a significant speed up in practice.